$\"\"$

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(a).

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The diffrential equation is $\"\"$ .

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Draw the graphs of solutions that satisfies the following initial conditions :

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$\"\"$ and $\"\"$ .

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(1).Draw the coordinate plane.

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(2). graph the diffrential equation $\"\"$ .

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Graph :

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When $\"\"$ .

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$\"\"$

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Graph : When $\"\"$ .

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$\"\"$

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Graph : When $\"\"$ .

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$\"\"$

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Graph : When $\"\"$ .

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$\"\"$

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$\"\"$

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(b).

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Find the equilibrium solutions :

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Equilibrium solutions are the conditions for which $\"\"$ .

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The diffrential equation is $\"\"$ .

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Therefore equilibrium solutions are the values of $\"\"$ for which :

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$\"\"$

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If $\"\"$ tehen the general solution is : $\"\"$ .

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Therefore, $\"\"$ .

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Multiply both sides by $\"\"$ .

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$\"\"$

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Where $\"\"$ is an integer.

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Therefore, the equilibrium solution of $\"\"$ is any even number.

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$\"\"$

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(a).

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Graph : When $\"\"$ .

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$\"\"$

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Graph : When $\"\"$ .

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$\"\"$

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Graph : When $\"\"$ .

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$\"\"$

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Graph : When $\"\"$ .

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$\"\"$

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(b).

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The equilibrium solution of $\"\"$ is any even number.